diff --git a/pybgl/functions/shamir.py b/pybgl/functions/shamir.py
index b61c7a0..7da2d74 100644
--- a/pybgl/functions/shamir.py
+++ b/pybgl/functions/shamir.py
@@ -89,6 +89,10 @@ def _interpolation(points, x=0):
 def split_secret(threshold, total,  secret):
     if not isinstance(secret, bytes):
         raise TypeError("Secret as byte string required")
+    if threshold < 2:
+        raise ValueError("threshold >= 2")
+    if total < threshold:
+        raise ValueError("total shares >= threshold")
     if threshold > 255:
         raise ValueError("threshold <= 255")
     if total > 255:
diff --git a/pybgl/test/shamir.py b/pybgl/test/shamir.py
index 1d31fa4..c0ebc36 100644
--- a/pybgl/test/shamir.py
+++ b/pybgl/test/shamir.py
@@ -58,6 +58,13 @@ def test_secrets(self):
             self.assertEqual(s, secret)
         print("Shamir secret sharing OK")
 
+    def test_split_secret_rejects_invalid_thresholds(self):
+        secret = b"wtw5heywrhsrhrtht"
+
+        for threshold, total in ((0, 3), (1, 3), (4, 3), (2, 0)):
+            with self.assertRaises(ValueError):
+                shamir.split_secret(threshold, total, secret)
+
     def test_mnemonic_secrets(self):
         m = entropy_to_mnemonic(generate_entropy())
         k = split_mnemonic(m, 3, 5)
@@ -76,4 +83,3 @@ def test_mnemonic_secrets(self):
 
 
 
-